Heartbleed and Two-Factor Authentication - Does it help

Along with all the hype about the heartbleed bug, I've been reading a lot of posts and articles that recommend (amongst other things) to enable Two-Factor Authentication (2FA) to all services that support it.

In general, having 2FA greatly increases your security, since you credentials are not bound to just a username/password pair (something you know), but also rely on something you have (a phone to receive text messages or a device/application that generates one-time tokens).

Is this the panacea and the solution to the heartbleed problem?

Two-Factor Authenication - What's the right way

Following the numerous compromises of accounts to various online services (with the most news-covered being the Twitter account compromises), more and more online services are providing means for Two-Factor Authentication (2FA).

Just as a short primer, authentication is the procedure a service has in order to verify that the user claiming to want to authenticate is actually the user which holds the account. A good simple example (of one-factor authentication) is a username/password combination. I authenticate to the service by providing my username/password combination, and since I am the only on that should know this, I am authenticated as being the owner of the account.

The big problem with the above is what happens if my credentials are stolen or compromised? Well, the service can be tricked by a third person, which can provide the valid username/password combination, into thinking that the third person is me! Granted, there are cases where this is actually desirable (such as shared accounts) but in the end, the result is the same; the service has no way to identify that the person between the chair and the keyboard (or behind the touchscreen nowadays) is the account holder.